In the following, we consider that only a single error event is occurred over the CC trellis. Note that this simplification is widely considered in the literature [1]}.
Therefore, we intend to find out all the possible legitimate FTN error sequences that are induced by a single error event in the CC trellis.
Without loss of generality, we consider CC codewords with information bit length \(K^{\prime }\) , which is long enough to contain all the possible codewords
covering the CC error events with a relatively small Hamming error weight \(w\) .
Define \(\mathbf {c},\mathbf {c}^{\prime } \in \mathcal {C}^{\prime }\)  as the instances of the \(2^{K^{\prime }}\)  legitimate codeword.
By listing all the possible codewords, we are able to find the CC error sequences corresponding to each single error event \(\varepsilon \)  and \(\mathbf {c}\) .
We use \(U(\mathbf {c}, \varepsilon ) = \lbrace \varepsilon | \mathcal {I}_{\varepsilon } = i, \mathcal {L}_{\varepsilon } = l, \mathcal {W}_{\varepsilon } = w \rbrace \)  to denote the set of possible single error events for a legitimate codeword \(\mathbf {c}\) , where each error event \(\varepsilon \)  in \(U(\mathbf {c}, \varepsilon )\)  has an event error length \(\mathcal {L}_{\varepsilon } = l\)  and the corresponding CC error sequence has Hamming error weight \(\mathcal {W}_{\varepsilon } = w\)  between \(\mathbf {c}\)  and \(\mathbf {c}^{\prime }\) , corresponding to \(\mathcal {I}_{\varepsilon } = i\)  different information bits.
